Aircraft: COMMERCIAL FIXED WING
Phase of flight: Initial Climb
Anomaly: Aircraft Equipment Problem Less Severe; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance

When I initially loaded the FMS I misspelled a waypoint. We went through the legs and thought they were right until we noticed the MFD was saying we would be landing with 0 fuel. The captain realized my error and reentered the flight route. After fixing the error we did not go back through all of the points and did not catch that there was no discontinuity after the departure like there should have been.We were climbing out of JFK on the Kennedy One Departure Canarsie climb. The flight director had us make the turn to the left like it should have; but then told us to turn right even though the departure has us continuing to the left to avoid LGA. The captain was familiar with the departure and knew there was something wrong when I started following the flight director to the right. He told me to turn back towards the left and contacted Departure asking us for a heading assignment and apologizing for the incorrect turn. Departure gave us a heading and later told us it wasn't a big deal and there were no LGA separation issues. As soon as we got the heading assignment the captain fixed my FMS and flight director. I should have been slower with initially entering the flight plan; we should also have reviewed all of the legs again after fixing my mistake. It was also good to learn that if you put in the departure before the first waypoint no discontinuity appears in the FMS. My first officer loaded the flight plan into the FMS; and after verifying the route with the route on the dispatch release; we noticed that the projected fuel on arrival was 0 lbs (ZERO). Since we already verified the route; I decided to re-enter the flight plan; and this corrected it. The problem happened to be a misspelling of the fix BENEE- it was originally entered as BENNE. When I entered the flight plan; I loaded the departure procedure before the route; which left us without the discontinuity. We did not recheck the flight plan.The fix that followed CRI on the departure was named CRI02. When we reached CRI; CRI02 was almost directly to our left (9 o'clock position). Climbing out of JFK on the Kennedy One departure; Canarsie Climb; we had a course deviation. When we got to CRI; the flight director commanded a right turn instead of a left turn. I noticed after take off that there was no discontinuity between the departure and our first fix- NEION. When I noticed the deviation; I told the pilot flying to turn back to the left and then asked ATC for a heading; and advised them that the autopilot ( I should have said flight director) turned us in the wrong direction. ATC asked us what climb we were given and I told him the CRI climb. He said to be careful with that due to LGA traffic. When making corrections to a flight plan in the FMS; I will re-verify the legs with my crew; to insure accuracy. Also; when I see the problem start to occur; I will take quicker appropriate action- in this case have the pilot flying go to heading mode and turn in the right direction; or even take the controls and correct it myself; explaining later what happened. Air carrier crew report misspelling a waypoint during FMC set up which is not detected until the FMC indicates landing with zero fuel. On the Kennedy One Departure CANARSIE climb it is not noticed that the route discontinuity after CRI is missing resulting in a turn toward the first flight plan waypoint. The Captain detects the wrong turn direction and requests ATC assistance.